Traditionally temporal phase unwrapping for phase measuring profilometry needs to employ the phase computed from unit-frequency patterned images; however, it has recently been reported that two phases with co-prime frequencies can be absolutely unwrapped each other. However, a manually man-made look-up table for two known frequencies has to be used for correctly unwrapping phases. If two co-prime frequencies are changed, the look-up table has to be manually rebuilt. In this paper, a universal phase unwrapping algorithm is proposed to unwrap phase flexibly and automatically. The basis of the proposed algorithm is converting a signal-processing problem into a geometric analysis one. First, we normalize two wrapped phases such that they are of the same needed slope. Second, by using the modular operation, we unify the integer-valued difference of the two normalized phases over each wrapping interval. Third, by analyzing the properties of the uniform difference mathematically, we can automatically build a look-up table to record the corresponding correct orders for all wrapping intervals. Even if the frequencies are changed, the look-up table will be automatically updated for the latest involved frequencies. Finally, with the order information stored in the look-up table, the wrapped phases can be correctly unwrapped. Both simulations and experimental results verify the correctness of the proposed algorithm.

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Published in Proceedings of SPIE, v. 10546, Emerging Digital Micromirror Device Based Systems and Applications X, article 105460B, p. 1-9.

© 2018 SPIE. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

Jianwen Song, Yo-Sung Ho, Daniel L. Lau, Kai Liu, "Universal phase unwrapping for phase measuring profilometry using geometry analysis," Proc. SPIE 10546, Emerging Digital Micromirror Device Based Systems and Applications X, 105460B (February 22, 2018). DOI: https://doi.org/10.1117/12.2289423

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This work was supported, in part, by the National Natural Science Foundation of China (#61473198) and by the Science and Technology Support Program of Sichuan Province, China (#18ZDYF1655).